Trimmed estimation in the measurement error model when the covariate has replicated observations

A measurement error model is considered with emphasis on the case where replicated measurements on the covariate are obtainable. Trimmed estimators of the coefficients in the model are defined based on the regression quantiles and the symmetric quantiles. The asymptotic distributions of these estimators are also obtained. On the basis of the criterion of asymptotic relative efficiency, these trimmed estimators are compared with the usual one and are found to be more efficient when random error in the regression equation has the contaminated normal distribution. A lower bound for the efficiency of the trimmed estimators derived by means of the regression quantiles is provided as well.